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Abstract

We have studied the effects of shutter transients (STs) in molecular beam epitaxy
(MBE). Two series of samples were grown by MBE and evaluated by X-ray diffraction
(XRD) and X-ray reflectivity (XRR) measurements. The effects of STs were evaluated
by growth rate (GR) analysis using a combination of growth time (GT) and thickness
evaluated by XRD and XRR measurements. We revealed two opposite effects of STs: (1)
overshoot of GR and (2) increase in GR with GT and subsequent saturation. Each effect
was consistent with the previous studies; however, the previous studies showed no
relationships between these two effects. By considering closing time of the shutter,
the two opposite effects were well understood.

Keywords:

Background

Molecular beam epitaxy (MBE) is an ideal method to grow nano-structures. MBE allows
for the controlled growth of films with sharp doping profiles and different chemical
compositions changing over a spatial depth of several angstroms. Multi-layer structures
with alternating doping (n, p, or intrinsic) or alternating band gaps can be grown.
In addition, self-organized effects can be applied for growing the nano-structures
with controlled dimensions that are not only in the growth direction (thickness) but
also laterally in the plane of the growth surface. These nano-structures are well
known as quantum wells (QWs), quantum wires, and quantum dots (QDs). When their sizes
are decreased, the quantum confinement effect becomes the dominant contribution to
their electric and optical properties. Because quantum confinement energy is inversely
proportional to size (1/L), accuracy of size is very important to fabricate the nano-structures.
However, MBE cannot avoid the effects of shutter transients (STs) by which a prominent
inaccuracies are caused by strong flux transients after opening the shutter due to
temperature gradients in the cells. In an MBE system, beam sources are provided by
thermal evaporation of solid source materials in the cells, and the beam sources are
individually controlled by mechanical shutters to obtain the intended structures.
The mechanical shutters also reflect heat back into the cells. Therefore, a temperature
gradient occurs when the mechanical shutters are moved. The studies conducted for
STs were contrasting in two ways: (1) growth rate (GR) decreased and was saturated
after a characteristic time constant (CTC) [1-4], and (2) the GR was below the desired GR and then approached the target GR within
the CTC [5,6]. Therefore, the effects of STs seemed to be contradictory or to have a machine dependence.
Therefore, we have studied the effects of STs for our MBE system.

Methods

Evaluation method of shutter transients

In order to evaluate STs for MBE, growth time (GT) dependence of GR must be evaluated.
Reflection high-energy electron diffraction (RHEED) in MBE is a powerful tool to evaluate
GR. During growth, the intensity of oscillation at a specular spot can be observed,
and 1 period of the oscillation corresponds to the growth of 1 mono-layer (ML). Evolution
of the oscillation can be used to evaluate the GT dependence of the GR. Previous studies
have used this method to evaluate STs [2,4,5]. However, GR evaluation using RHEED has some drawbacks. The oscillation is damped.
Although substrate rotation is required to obtain good thickness uniformity on the
samples, substrate rotation is not possible during RHEED oscillation measurements.
This means that only one position in the sample is measured, and thus, some error
is involved in this method. In addition, observation of the oscillation is strongly
dependent on the growth condition. To overcome these drawbacks, in the present study,
some samples were grown, and then the thickness of the samples was evaluated using
X-ray diffraction (XRD) and reflectivity (XRR) measurements. XRD measurements can
be used to evaluate the layer thickness when the sample has a periodic structure.
Because of satellite peak patterns, separation that corresponds to the period can
be distinguished. On the other hand, XRR measurements do not require a periodic structure
to evaluate thickness. To evaluate the thickness of individual layers by XRR, model-based
fitting is required. Because the GT of the samples is known, the GR can be calculated.
In this study, InGaAs layers were targeted to evaluate the GT dependence of the GR.

Experiments

Our MBE system (VG-V80H) was equipped with solid sources of Al, Ga, As, P, and two
sources of In(1,2). Al, Ga, and In(1) were standard VG cells, while In(2) was a dual-filament
cell provided by Veeco Instruments, Inc. (St. Paul, USA). As and P were valved cracking
cells where the cracking temperatures were 900°C. We grew two series of the samples
to consider the properties of both measurements as discussed in the previous section.
The first series used sets of two stacked superlattices (SLs) for XRD measurements,
and the second series used a set of coupled double quantum wells (CDQWs) for XRR measurements.
Each series was grown the same day to minimize fluctuations in the flux of the sources.
All samples were grown at 460°C. XRD spectra were taken under the symmetric [004]
reflection geometry using a high-resolution XRD system with a four-crystal monochromator.
XRR spectra were taken using the same system with a parallel plate collimator. SL
and CDQW samples consisted of In0.4Al0.6As and In0.72Ga0.28As layers, and In0.8Ga0.2As and AlAs layers, respectively. The difference in the In content of the InGaAs between
the SL and CDQW samples was due to strain compensation condition between the two layers.
The schematic structure of the samples is shown in Figure 1. For the SL samples, only In(1) was used. GT for the InGaAs was only varied for 10
s between the two stacked SLs for aiming to evaluate the GR at a fixed GT by subtracting
the periods of the stacked two SLs. Growth interruption (GI) between InGaAs and InAlAs
was set at 5 s for the SL samples. The number of stacks for the two stacked SLs was
different to distinguish each period by taking into account of full width at half
maximum (FWHM) of the diffraction peaks. Conversely, GT was the same for the two InGaAs
layers of CDQWs. However, two In cells were used individually for a bottom InP buffer
of 50 nm and labeled CDQW(1) and CDQW(2) as shown Figure 1. GIs were set at 5 s for the As/As interface and 10 s for As/P interface of the CDQWs,
respectively. Because the evaluation of XRR measurements was based on fitting, CDQW
samples were evaluated by photoluminescence (PL) measurements to check the accuracy
of the evaluation. PL spectra were taken under a 514.5 nm Ar ion excitation laser
at 77 K.

Figure 1.Schematic structure of the samples. (a) Superlattice samples with InGaAs growth time ‘a’ and InAlAs growth time ‘b’. (b) CDQW samples with growth time for InGaAs and In cells used for this growth.

Results and discussion

Superlattice samples

XRD spectra of the samples are shown in Figure 2. Sharp and strong peaks at the center of each spectrum correspond to InP substrate.
Two sets of the periodic peaks with different FWHMs were distinguished. When the GT
of InGaAs was long, the difference in the periods between two SLs was small. This
made it difficult to find each of the two peaks in the SLs. However, the difference
in periods was clearly distinguishable among the higher satellite peaks. These differences
in periods for all samples were used to calculate GR. Figure 3 shows GT dependence of GR for InGaAs. It can be seen that GR was initially low and
then increased with GT by a factor of up to 14% during GT testing. Particularly, GR
was increased almost 10% when GT was 30 to 60 s. This dependence was consistent with
the studies [5,6]. Therefore, the dependence can be understood as the effect of STs. The effect could
be attributed as follows: when the shutter was opened, heat radiation from the cell
instantly lowered the surface temperature of the source located at inside the cell
(Tsurface). Then, Tsurface was increased due to stabilization in the entire cell structure.
These changes in Tsurface were responsible for the GT dependence of GR. It should
be noted here that the difference in GT of InGaAs was only 10 s between the two stacked
SLs. Consequently, estimated GR for shorter GT should have errors.

Figure 3.Growth time dependence of growth rate for InGaAs. The growth rate is determined by the differences in the SL periods between the two
stacked SLs.

Coupled double quantum well samples

Figure 4 shows XRR spectra of CDQW samples. Due to the identical structure of the two CDQWs
and the same growth condition, these CDQWs should have exhibited identical spectra
in XRR measurements. However, the spectra revealed slight periodic differences for
higher angles that indicated structural differences between the two CDQW samples.
To evaluate their structures, simulations for XRR spectra were performed. Results
of comparing the simulations with experimental XRR spectra are shown in Figures 5a,b; the fitting results are listed in Table 1. For the simulations, the model structure was almost the same as the intended structure
as shown Figure 1b. The only difference was that a surface oxide layer was added to the model structure.
Sample size and X-ray beam width and divergence were also included in the simulation
because these parameters were critical due to the glancing angle of the incident X-ray
beam in the XRR measurements. The simulation spectra agreed well with the experimental
spectra; therefore, the simulations were successful. The simulation results listed
in Table 1 show that the thicknesses of the top InP layer and the InGaAs layers were different,
although the intended structure was identical between the two CDQWs. Due to the sensitivity
of the surface to XRR measurements, the topmost layer was difficult to evaluate [7]. Therefore, the difference in structure was mainly due to the thicknesses of the
InGaAs layers. The bottom InGaAs layer was thicker than the upper layers. Due to the
same time for growing InGaAs, GR of InGaAs layers exhibited overshoot. This behavior
was consistent with the studies [1-4] that revealed flux or GR overshoot. Figure 6 shows PL spectra of the CDQW samples. The spectra revealed the PL peaks were 0.89
and 0.84 eV for CDQW(1) and CDQW(2), respectively. This difference in their peaks
was consistent with their structures because the bottom InGaAs layer was thicker for
CDQW(2) compared with CDQW(1). The increase in thickness of the bottom InGaAs layer
was larger in CDQW(2) sample. The difference in the growth conditions between CDQW(1)
and CDQW(2) was the In cell that was used for growing the InP buffer layer. Due to
the growth condition, the In(1) and Ga cells were opened first to grow the bottom
InGaAs layer of CDQW(2), whereas only the Ga cell was opened first for CDQW(1). Therefore,
the flux overshoots of both In(1) and Ga cells occurred to grow InGaAs of CDQW(2),
whereas only the Ga cell was under the flux overshoot for growing InGaAs of CDQW(1)
that was responsible to the increase in thickness of bottom InGaAs. The flux overshoot
could be related with the change in Tsurface. Tsurface was slightly higher than the
desired temperature when closing time of the shutters was long, because the shutter
reflected the heat back into the cell and because the thermocouple for the cell was
located outside of crucible of sources. On the other hand, Tsurface was lowered by
the temperature gradient due to the opening of the shutter. These changes in Tsurface
for the In and Ga cells could be attributed to the flux overshoot.

Consideration of shutter transients

We observed two opposite types of STs in the previous two sections. First was the
increase in GR with GT, and second was the overshoot of GR. These behaviors were inconsistent
with each other. The difference between the two experiments was the sample structure
and the evaluation method. The first was the stacked SLs with XRD measurements, and
the second was the single CDQW with XRR measurements. Because XRD measurement of the
stacked SLs revealed an average GR for the whole structure, while the XRR measurements
of the single CDQW revealed an initial state of growth, the two opposite behaviors
could be attributed to long or short shutter closing times. Therefore, the effects
of STs in MBE involved two opposite behaviors depending on the shutter closing time.
However, Celii et al. [4] reported that STs for their MBE system only showed the overshoot of GR whose amplitude
and decay time were related with the shutter closing time. On the other hand, other
studies [1-3,5,6] reported one type of STs without the consideration of the shutter closing time. Due
to the fact that the effects of STs were strongly dependent on the MBE system, our
observations of the two types of STs were characteristics of our MBE system because
an amount of the heat back into the cell must depend on the whole structure of the
cells. However, the origin of STs arose from the temperature gradient in the cell
when the mechanical shutter was moved. This origin is not avoided; therefore, the
effects of STs can be said that there is universal phenomena in the MBE system. It
should be noted here that our evaluation methods for the effects of STs were different
with respect to the previous studies [1-6]. The main difference was that XRR measurement was used to evaluate STs for the initial
state of growth. The previous studies used to evaluate STs for their MBE systems as
following: beam flux measurements [1], RHEED measurements [2,5,6], optical absorption measurements of QW samples, reflection mass spectroscopy [3], and XRD measurements of SL samples [6]. These measurements as well as XRR measurement are powerful methods to reveal the
effects of STs, but each measurement has some drawbacks. The drawbacks for RHEED measurements
have already been pointed out in the previous section. However, XRD and XRR measurements
which were used in this study have a merit of high accuracy of thickness evaluation.
In addition, XRR measurement does not require the periodic structure like SLs which
are used for XRD measurement. This feature is very important to reveal the initial
state of growth as mentioned before. Therefore, a combination of the evaluation methods
used in this study is well balanced and suitable to reveal an entire feature of STs.
On the other hand, our experimental results revealed that 5% to 10% of the error in
the thickness easily occurred for the designed structure at around 3 nm. Therefore,
the effects of STs should be carefully taken into account if the size of the intended
structure is as small as a few nanometers.

Conclusions

We have studied the effects of STs in MBE, and two opposite effects were found. Each
effect was consistent with previous studies; however, the previous studies showed
no relationships between them. Our experimental results could be categorized into
two situations: long and short closing times of the shutters. By categorizing these
situations, the two opposite effects were understood. Finally, we pointed out that
the effects of STs should be carefully taken into account if the size of the intended
structure is as small as a few nanometers.

Competing interest

The authors declare that they have no competing interests.

Authors’ contributions

SG carried out the MBE growth, the XRD, XRR, and PL measurements, and wrote the manuscript.
TM supported the PL measurements, participated in the analysis of the experimental
results, and discussed the results. HK and HI discussed the results. All authors read
and approved the final manuscript.